A note on discrete Heisenberg uniqueness pairs for the parabola

We discuss on Heisenberg uniqueness pairs for the parabola given by discrete sequences along straight lines. Our method consists in linking the problem at hand with recent uniqueness results for the Fourier transform.Comment: 6 page

New Sign Uncertainty Principles

We prove new sign uncertainty principles which vastly generalize the recent developments of Bourgain, Clozel & Kahane and Cohn & Gon\c{c}alves, and apply our results to a variety of spaces and operators. In particular, we establish new sign uncertainty principles for Fourier and Dini series, the Hilbert transform, the discrete Fourier and Hankel transforms, spherical harmonics, and Jacobi polynomials, among others. We present numerical evidence highlighting the relationship between the discrete and continuous sign uncertainty principles for the Fourier and Hankel transforms, which in turn are connected with the sphere packing problem via linear programming. Finally, we explore some connections between the sign uncertainty principle on the sphere and spherical designs.Comment: 45 pages, 2 figures, 3 tables, v3: typos corrected, numerics extende

Wild dogs at stake: deforestation threatens the only Amazon endemic canid, the short-eared dog (Atelocynus microtis)

The persistent high deforestation rate and fragmentation of the Amazon forests are the main threats to their biodiversity. To anticipate and mitigate these threats, it is important to understand and predict how species respond to the rapidly changing landscape. The short-eared dog Atelocynus microtis is the only Amazon-endemic canid and one of the most understudied wild dogs worldwide. We investigated short-eared dog habitat associations on two spatial scales. First, we used the largest record database ever compiled for short-eared dogs in combination with species distribution models to map species habitat suitability, estimate its distribution range and predict shifts in species distribution in response to predicted deforestation across the entire Amazon (regional scale). Second, we used systematic camera trap surveys and occupancy models to investigate how forest cover and forest fragmentation affect the space use of this species in the Southern Brazilian Amazon (local scale). Species distribution models suggested that the short-eared dog potentially occurs over an extensive and continuous area, through most of the Amazon region south of the Amazon River. However, approximately 30% of the short-eared dog's current distribution is expected to be lost or suffer sharp declines in habitat suitability by 2027 (within three generations) due to forest loss. This proportion might reach 40% of the species distribution in unprotected areas and exceed 60% in some interfluves (i.e. portions of land separated by large rivers) of the Amazon basin. Our local-scale analysis indicated that the presence of forest positively affected short-eared dog space use, while the density of forest edges had a negative effect. Beyond shedding light on the ecology of the short-eared dog and refining its distribution range, our results stress that forest loss poses a serious threat to the conservation of the species in a short time frame. Hence, we propose a re-assessment of the short-eared dog's current IUCN Red List status (Near Threatened) based on findings presented here. Our study exemplifies how data can be integrated across sources and modelling procedures to improve our knowledge of relatively understudied species